List of paradoxes
Not all paradoxes fit neatly into one category. Some paradoxes include:
Veridical paradoxes
These are unintuitive results of correct logical reasoning.
Mathematical/Logical
- Apportionment paradox: Some systems of apportioning representation can have unituitive results
- Alabama paradox
- New states paradox
- Population paradox
- Averaging - the mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results - for example, it is possible that moving an entry from Wikipedia to Wiktionary would increase the average entry length on both sites - Will Roger's phenomenon
- Arrow's paradox/Voting paradox/Codorcet paradox: You can't have all the attributes of an ideal voting system at once
- Banach-Tarski paradox: Cut a ball into 5 pieces, re-assemble the pieces to get two balls, both of equal size to the first.
- Birthday paradox: What is the chance that two people in a room have the same birthday?
- Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number which is smaller than itself.
- Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured on the roof, and disassembled in the basement.
- Galileo's paradox: Though most numbers are not squares, there are no more numbers than squares.
- Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests.
- Monty Hall problem: An unintuitive consequence of conditional probability.
- Monty Hell problem: Positive daily profits yield zero assets in the limit.
- Raven paradox (or Hempel's Ravens): Observing a red apple increases the likelihood of all ravens being black.
- Richard's paradox: A complete list of definitions of real numbers doesn't exist.
- Simpson's paradox: An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.
- Statistical paradox: It is quite possible to draw wrong conclusions from correlation. For example, towns with a larger number of churches generally have a higher crime rate - because both result from higher population. A professional organization once found that economists with a PhD actually had a lower average salary than those with a BS - but this was found to be due to the fact that those with a PhD worked in academia, where salaries are generally lower.
Psychological/Philosophical
- Abilene paradox: People take actions in contradiction to what they really want to do, and therefore defeat the very purposes of what they were trying to accomplish.
- Control paradox Man can never be free of control, for to be free of control is to be controlled by oneself.
Physical
- Braess' paradox: sometimes adding extra capacity to a network can reduce overall performance
- Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics?
- Twin paradox: When the travelling twin returns, he's younger and older than his brother who stayed put.
- Zeno's paradoxes: When you reach the turtle's spot, it has already advanced a bit, so you can never catch it.
Falsidical paradoxes
These are incorrect results of subtly false reasoning.
Antinomies
Paradoxes that show flaws in accepted reasoning, axioms, or definitions. Note that many of these are special cases, or adaptations, of the Russell's paradox.
- Barber paradox: The barber who shaves all men who don't shave themselves, and no-one else.
- Berry paradox: What is "The first number not nameable in under ten words"?
- Curry's paradox: "If I'm not mistaken, the world will end in a week."
- Grelling-Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word?
- Liar paradox: "This sentence is false."
- Quine's Liar Paradox: "Yields a falsehood when appended to its own quotation."
- Russell's paradox: Is there a set of all those sets that do not contain themselves?